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If Tanisha has $1000 to invest at 7% per annum compounded semiannually, how long will it be before she has $1600? If the co

Sphinxa [80]

Answer:

Using continuous interest 6.83 years before she has $1600.

Using continuous compounding, 6.71 years.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

Continuous compounding:

The amount of money earned after t years in continuous interest is given by:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial investment and r is the interest rate, as a decimal.

If Tanisha has $1000 to invest at 7% per annum compounded semiannually, how long will it be before she has $1600?

We have to find t for which $A(t) = 1600$ when $P = 1000, r = 0.07, n = 2$

$A(t) = P(1 + \frac{r}{n})^{nt}$

$1600 = 1000(1 + \frac{0.07}{2})^{2t}$

$(1.035)^{2t} = \frac{1600}{1000}$

$(1.035)^{2t} = 1.6$

$\log{1.035)^{2t}} = \log{1.6}$

$2t\log{1.035} = \log{1.6}$

$t = \frac{\log{1.6}}{2\log{1.035}}$

$t = 6.83$

Using continuous interest 6.83 years before she has $1600

If the compounding is continuous, how long will it be?

We have that $P(0) = 1000, r = 0.07$

Then

$P(t) = P(0)e^{rt}$

$1600 = 1000e^{0.07t}$

$e^{0.07t} = 1.6$

$\ln{e^{0.07t}} = \ln{1.6}$

$0.07t = \ln{1.6}$

$t = \frac{\ln{1.6}}{0.07}$

$t = 6.71$

Using continuous compounding, 6.71 years.

7 0

3 years ago

Please help me out! I have lots of work to do and if you help it will relieve the stress.

Nina [5.8K]

Answer:

<h2>2. Combining old and new observations.</h2>

Step-by-step explanation:

Through the passage, Nicholas Copernicus is introducing to the reader a new worlds, based on observations from the pass, and recent observations made by scientists. Basically, he's talking about a work where the reader is going to able to learn and be aware about the stars and planets movements in a way that no one could imagine before.

Copernicus specifically states that those observations are based on ancient and new data.

Therefore, the right answer is 2, because it's a combination of old and new observations.

3 0

4 years ago

PLEASE THIS IS MY LAST TRY PLEASE

FrozenT [24]

Hope this helps :) good luck!!!

5 0

3 years ago

Read 2 more answers

A parabola can be represented by the equation x2 = 2y. What are the coordinates of the focus and the equation of the directrix?

Airida [17]

Answer:

b)

i) Focus ( 0,a) = $(0,\frac{1}{2} )$

ii) The equation of the directrix is

$y = -\frac{1}{2} or y +\frac{1}{2} =0$

Step-by-step explanation:

Step(i):-

A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point (not in a line) in the plane

• The Fixed line is called the directrix of the parabola.

• The Fixed point is called the focus of the parabola.

• A line through the focus and perpendicular to the directrix is called the axis of the parabola.

• The point of intersection of parabola with the axis is called the vertex of the parabola.

Given Parabola x² = 2 y

Comparing x² = 4 a y

4 a = 2

$a = \frac{1}{2}$

Focus ( 0,a) = $(0,\frac{1}{2} )$

Step(ii)

The equation of the directrix is y = -a or y +a=0

The equation of the directrix is

$y = -\frac{1}{2} or y +\frac{1}{2} =0$

The equation of the directrix is 2 y +1 =0

6 0

3 years ago

If f(x) is a continuous function defined for all real numbers, f(–10) = –2, f(–8) = 5, and f(x) = 0 for one and only one value o

Vinvika [58]

F(-10)=-2, f(-8)=5, and f is continuous. All these mean that f(x) is 0 for x in between -10 and -8.

That is, f at -10 is negative, then at -8 is positive. So the graph of f "cuts" the x-axis for an x value in (-10, -8).

Since there is only one value such that f(x)=0, x can only be -9.

Answer: -9

8 0

3 years ago